Title:
Dynamical Density Fluctuations around QCD Critical Point Based on Dissipative Relativistic Fluid Dynamics-possible fate of Mach cone at the critical point-

Abstract: We study the dynamical density fluctuations around the QCD critical point(CP)
using dissipative relativistic fluid dynamics in which the coupling of the
density fluctuations to those of other conserved quantities is taken into
account. We show that the sound mode which is directly coupled to the
mechanical density fluctuation is attenuated and in turn the thermal mode
becomes the genuine soft mode at the QCD CP, which is actually known for the
non-relativistic case. We give a speculation on the possible fate of Mach cone
in the vicinity of the QCD CP as a signal of the existence of the CP on the
basis of the above finding. It is also shown that relativistic effects appear
differently according to the choice of the frame in which the flow velocity is
defined. We clarify that the so called first-order relativistic fluid dynamic
equations have generically no problem to describe fluid dynamical phenomena
with long wave lengths contrary to a naive suspect whereas even Israel-Stewart
equation, a popular second-order equation, may not describe the fluid dynamical
mode in general depending on the value of the relaxation time.